A generalization of the Montgomery Hooley theorem

被引：1

作者：

Yao, Weili ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2016年 / 162卷

关键词：

Circle method; Exponential sums; Selberg-Delange method; DAVENPORT-HALBERSTAM THEOREM; ARITHMETIC PROGRESSIONS; PRIMES; VARIANCE; NUMBER;

D O I：

10.1016/j.jnt.2015.10.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Omega(n) be the total number of prime factors of n and Theta(k)(x;q,a) = Sigma(n <= x) (Omega(n)=k) 1, where k is allowed to tend to infinity with respect to x. Combining the circle method with the Selberg Delange method, together with the result of Bombieri-type sum for exponential sums, we investigate the behavior of the error term of 0, (x; q, a) in the "mean" and obtain its upper bound. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：496 / 517

页数：22

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